In Chapter 1, I present empirical research on proto-arithmetical abilities, that is, subitising and estimating, and emphasise the importance of distinguishing them from arithmetical abilities. I review the empirical literature on the cognitive basis of proto-arithmetical abilities, focusing mostly on the core cognitive theory of the object tracking system (OTS) and approximate numerosity system (ANS). Although the topic requires further research, I proceed with the view that the OTS and ANS are different cognitive systems and are responsible for the subitising and estimating abilities, respectively.